Final Exam Review F 06 M 236 Be sure to look over all of your tests, as well as over the activities you did in the activity book

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1 inl xm Review 06 M 236 e sure to loo over ll of your tests, s well s over the tivities you did in the tivity oo 1 1. ind the mesures of the numered ngles nd justify your wor. Line j is prllel to line. 6 j Without using formul, explin nd illustrte how to find the sum of the mesures of the interior ngles of this polygon.. Next provide formul tht n e used to find the sum, nd explin wht ll of the numers nd letters represent.. Wht is the sum of the exterior ngles of this polygon? d. This is regulr polygon. ind the mesure of vertex ngle, nd find the j 57 mesure of n exterior ngle. e. The seond polygon is not regulr polygon. Wht prts d n you nswer out this polygon? nswer ny questions you n. 3.. Is it true tht m( 1) + m( 2)= m( 4) for this tringle? Why or why not?. If m( 2) = 60 = m( 3), wht re ll of the things you now out this tringle? student sys regulr polygon is polygon with ll sides ongruent, is this enough informtion to onlude tht the polygon is regulr? 5.. Note the three lines j,, nd m re prllel. ind the mesure of ngle. 6. Shown re some tringles. ongruent sides re indited. irle ll the numers orresponding to nmes tht desrie the figure (you will wnt to go nd review doing the sme thing with qudrilterls!!) 1. slene 2. isoseles 3. ute 5. otuse 6. right rw n exmple of eh of the following:. Isoseles trpezoid. onve hexgon. qudrilterl tht is oth ite nd prllelogrm. d. prllelogrm tht is not squre or retngle. e. qudrilterl tht hs 180 rottionl symmetry (only) nd one line of symmetry. 68 j m j m

2 8. rw in the lines of symmetry for these polygons If polygon hs rottionl symmetry, list the symmetries nd drw in one turn ngle. regulr 9. Whih of the following re true? ) if figure is retngle, then it is lso prllelogrm. ) if figure is rhomus, then it is lso squre. ) if figure is squre, then it is retngle nd rhomus. d) if figure is rhomus, it is prllelogrm nd ite e) if figure is prllelogrm, then opposite sides re ongruent f) if qudrilterl hs opposite sides ongruent, then it is prllelogrm g) the digonls of prllelogrm iset eh other h) the digonls of rhomus iset eh other i) if figure is prllelogrm, then opposite ngles re ongruent j) the digonls of rhomus iset the vertex ngles nd re perpendiulr 10. Whih of the following pitures of sets est represents eh of the following reltionships. LL TH STS.. etween trpezoids nd prllelogrms? ii. rhomi nd retngles i. etween retngles nd squres? 11. ) Stte uler s formul tht relted the numer of verties, sides nd fes of polyhedron. ) Nme this polyhedron, nd demonstrte uler s formul for this solid. ) IN regulr polyhedron, the sme numer of fes meet t eh vertex nd ll fes re ongruent regulr polygonl regions. Whih of these polyhedr re regulr polyhedr (ssume ll fes re regulr polygonl regions) If it is regulr polyhedr, nme it.... iii 12.. ive the most omplete nme for the following polyhedrons.... I H J L K

3 13. etermine if the following tringles re ongruent, if so justify your response nd provide the pproprite ongruene property, if not lso justify your response. If the tringles re ongruent, provide orret ongruene sttement for the tringles... IK is perpendiulr isetor of HJ I K J Q H N L 100 P. d. iven tht segment isets, prove tht M R 14.. The onditions PQ MN, PR MO, nd Q N re suffiient to prove tht ΔPQR ΔMNO.. If for two tringles, ΔPQR nd ΔMNO, we now tht PQ MN. Wht else would we need to now to onlude tht the tringles re ongruent y SS 15 Provide resons for eh of the following steps in this proof. 2 The sum of the interior ngles of tringle is 180 degrees. onstrut line through point prllel to m( 4) + m( 3) + m( 5) = 180 d. m( 1) + m( 3) + m( 2) = Is the re of these two tringles the sme or different? ive n explntion tht does not inlude omputing the re of the two tringles. 1 unit 17. ind the re of these polygons. lerly show ll of your wor. 1 unit 18. ill in the lns dm 2 = m m = m

4 0.627 g = mg 28,000,000 m 3 = m ml = m L of wter hs mss of g or g m = m 2.9 m 3 = mm This figure represents one of our justifitions of the Pythgoren Theorem. If Squre 1 nd Squre 2 hve the sme re nd we remove the 4 shded tringles from Squre 1 nd Squre 2 - explin why this is n illustrtion of the Pythgoren theorem. e sure to stte the Pythgoren theorem in your explntion. squre 1 squre right isoseles trpezoidl prism hs height 8 m. The ses re isoseles trpezoids with prllel sides of length 11 m nd 5 m nd height of 6 m. ind the surfe re. Show lerly eh surfe you re finding re of nd the relted omputtions. Then find the volume. 5 m Seth the pyrmid whose volume you ould find using this prism. ind the volume. 8 m 21. If ontiner ( right squre pyrmid with height 12 m nd se with side lengths = 12 m) is filled with wter, nd then the wter is poured into ontiner ( ue of side 12 m) i. How full will ontiner will e? ii. If the volume of ontiner is 728 m 3, wht is the volume of ontiner? Wht would the volume of ontiner e in: grms, ml, g, liters, nd dm 3? 12 m 11 m 12 m 12 m 22.. ind the surfe re nd volume of this ylinder. Show lerly nd step y step the surfes you re finding the res of nd the omputtions for eh.. rw nd lel one whose volume we ould find, given tht we now the volume of the ylinder in prt. ind the volume of this one. 3 m 10 m

5 23.. ind the volume of sphere with rdius of 7 m. lerly show ll of your wor nd explin riefly wht you re doing to find the volume.. How is the volume of this sphere relted to the volume of this ylinder? xplin how you now this from the rie experiment. 2r vse is in the shpe of right retngulr prism with dimensions of: se 20 m y 10 m nd with height of 15 m. You fill it to the top with wter.. rw piture of the prism nd lel it. ind the volume of wter it will hold in: i. m 3 ii. dm 3 iii. liters iv. find the mss of wter it will hold in: g _ g r. rw the pyrmid whose volume we ould find if we now the volume of the prism. 24. h of the following re right irulr ones.. ind the rdius r nd find the volume of the one. Show ll of your wor lerly. If you hve to use uddy solid, drw it Lines j nd re prllel. j 4 m 2 m 3.5 m H I ind the re of. Tringle prllelogrm. retngle HIJK 26. ind the re nd perimeter of this trpezoid. 2 m 7m 5m 2 m K 3 m J 27. Whih of the following hs the smllest volume? hexgonl prism with se re of 6 m 2 nd height of 2 m, Squre pyrmid with height of m nd se re of 4 m 2. right irulr one with se re of 6 m 2 nd height of 3 m. 11m 28.. If rdius of irle is 4 m, wht is its irumferene?. If the irumferene of irle is 12π in. wht is its rdius? imeter? 29. ssume you now the formuls for the re of prllelogrm explin, using pper nd sissor ides, how to develop the formuls for the res of tringles, then trpezoids. e sure to drw pproprite pitures nd lel them. 30. ind the re nd perimeter of this tringle. o not use sutrtion or ddition of res to find the re of the tringle. 31. ind the surfe re of the retngulr pyrmid to the nerest whole squre meter. Points nd iset their respetive sides of the se. ind the volume of this pyrmid. 4m 6m 8m

6 32. e redy to do one or two of the following proofs:. In n isoseles tringle, the ngles opposite the ongruent sides re ongruent. Wht we n lso show from this is tht the line tht is the medin, is lso the ltitude (or height).. retngle is lso prllelogrm.. Opposite sides of prllelogrm re ongruent. 33. Loo over the tivity, nd the test question in whih you hve to rete vrious polygons with the pproprite re e redy to do few of those. 34. One prolem on the homewor tht people seemed in generl to miss ws: If the perimeter of retngle inreses, does the re utomtilly inrese s well? Yes or no nd provide ny neessry exmples or ounterexmples. 35. True or lse. etermine if the following re true or flse. If flse, see if you n orret it or provide ounterexmple.. In igure 2, m( 1) + m( 2) = m( 4). 1. The mode of olletion of dt is the middle sore igure 2. Refer to the figure. If = = 8dm nd = = 5 dm then Δ Δ y SSS. d. The onditions PQ MN, PR MO, Q N re suffiient to prove ΔPQR ΔMNO. e.. Refer to the figure. If m( ) = 30 nd m( ) = 30 nd = = 3 units then Δ Δ y S. f. It is possile to hve dt suh tht the men equls the medin nd the medin is less thn the mode. g. Refer to the figure. Δ Δ y S h. If full ontiner of wter hs mss of 50 g, then the volume of the ontiner is 50 liters. i. If right irulr ylinder nd prism hve equl heights nd the res of their ses re equl then their volumes re equl. 3 3 j. Refer to igure 7. is prllelogrm nd = 10 m, = 5 m, nd = 4 m.. The distne x is 8 m 4 m x. This right pentgonl prism hs five lterl fes How mny edges, fes nd verties does it hve? 10 m igure 7 l. In regulr polyhedron the sme numer of fes meet t eh vertex. 5 m m. The digonls of rhomus iset the vertex ngles nd re perpendiulr.

7 36. n. XPNSS 20% 30% 15% 10% 25% If student udgets her money s indited y the irle grph, how muh of her weely $170 goes for food? () $30 () $51 () $56.67 (d) None of,, or. 37. The following ox nd whiser plot shows the sores of history test. Whih of the following sttements re true out the sores? I. The men sore on the test ws 60. II. The rnge of sores on the test ws 70. III. out 25% of the students sored 90 or etter. IV. out hlf the students sored etween 30 nd 60. () Only I nd II. () Only II, III, nd IV. () Only III nd IV. (d) None of the ove The shded figure is regulr pentgon. Wht does m( ) + m( ) + m( ) + m( ) + m( ) equl? () m( ) + m( ) + m( ) + m( ) + m( ) = 360 () m( ) + m( ) + m( ) + m( ) + m( ) = 180 () m( ) + m( ) + m( ) + m( ) + m( ) = 108 (d) none of the ove. 39. Let 1 e the length of shorter digonl H. Let 2 e the length of the longer digonl. The formul for the re of the ite in terms of the lengths of its digonls is : H () 1 x 2 () 1 2 ( 1 x 2 ) () 1 2 ( ) (d) None of the ove.

8 40. The lines l nd m re prllel. = = LM = 2 m, = 3.5, HI = 3 m, nd = 4 m. Wht is the sum of the res of the tringle, prllelogrm, nd retngle HIJK? K J L l () 14 m 2 () 15 m 2 () 17 m 2 (d) None of the m H M ove. I 41. Whih of the following is (re) true? (i) If figure is retngle, then it is lso prllelogrm. (ii) If figure is rhomus, then it is lso squre. (iii) If figure is squre, then it is retngle nd rhomus. 42. The men (or verge) of this set of dt is. The medin of this set of dt is. Weights of Students in st Junior High lger 1 lss note 10 3 represents 103 ls 42. If ertin polyhedron hs 10 verties nd 9 fes, then it hs edges m 3 of wter hs mss of g 3.5 dm 3 = L 32 ml of wter hs mss of g 44. Refer to the figure.. If the sphere of rdius 2 m is filled with wter nd poured in the right irulr ylinder with se of rdius 2 m nd height of 4 m, then the ylinder will e full of wter. 4 m 4 m 2 m 2 m 45. g ontins 2 red lls, 3 lue lls, nd 1 yellow ll.. Wht is the proility of drwing 1 red ll?. How mny red lls must e dded to the g so tht the proility of drwing red ll is 1 2? 46. Two oxes re set up t shool fir. The first hs one Red ll nd one reen ll. The seond ox hs 2 Red lls, 2 reen lls, nd 1 yellow ll.. How mny different outomes re in the smple spe for this experiment?. ive the smple spe for this experiment. R R2 R rw tree digrm for the experiment. Lel the proilities long eh rnh. Y